Question 115517
a)

Horizontal Asymptote:


Since the degree of the numerator (which is {{{1}}}) is less than the degree of the denominator (which is {{{2}}}), the horizontal asymptote is always {{{y=0}}}


So the horizontal asymptote is {{{y=0}}}


Vertical Asymptote:


To find the vertical aysmptote(s), set the denominator equal to zero:


{{{x^2+2=0}}} Set the denominator equal to zero



{{{x^2=-2}}} Subtract 2 from both sides



{{{x=sqrt(-2)}}} Take the square root of both sides


Since you cannot take the square root of a negative number, the answer is not a real number. So in this case, there are no vertical asymptotes